Which pair(s) of functions are inverses? There may be more than one correct answer.
a.) f(x) = x - 12, g(x) = x + 12
b.) f(x) = 3x, g(x) = 1/3x
c.) f(x) = 4x, g(x) = -4x
d.) f(x) = 2x + 1, g(x) = 2x - 1
My answer: B & C
b
the inverse is the reciprocal of a number.
5 inverse is 1/5
To determine whether two functions are inverses of each other, we need to check if performing one function and then the other brings us back to the original value.
Let's go through each pair of functions to see if they satisfy this condition:
a.) f(x) = x - 12, g(x) = x + 12
To find the composition of these functions, we substitute g(x) into f(x) or f(g(x)):
f(g(x)) = (x + 12) - 12 = x
Even though f(g(x)) equals x, g(f(x)) does not simplify back to x. Therefore, these functions are not inverses.
b.) f(x) = 3x, g(x) = 1/3x
Taking the composition:
f(g(x)) = 3(1/3x) = x
Similarly, g(f(x)) = 1/3(3x) = x
Hence, f(x) = 3x and g(x) = 1/3x are inverses.
c.) f(x) = 4x, g(x) = -4x
For the composition:
f(g(x)) = 4(-4x) = -16x
g(f(x)) = -4(4x) = -16x
So, f(x) = 4x and g(x) = -4x are inverses.
d.) f(x) = 2x + 1, g(x) = 2x - 1
Taking the composition:
f(g(x)) = 2(2x - 1) + 1 = 4x - 1
g(f(x)) = 2(2x + 1) - 1 = 4x + 1
Since f(g(x)) does not equal x and g(f(x)) does not equal x, these functions are not inverses.
Therefore, the correct pairs of functions that are inverses are b.) f(x) = 3x, g(x) = 1/3x and c.) f(x) = 4x, g(x) = -4x.